A coherent sinusoidal detector using phase compensation

A novel detector using phase compensation of spectrum observations is presented in this paper for detecting sinusoidal signals (or tonals) with unknown amplitude, frequency and phase in complex Gaussian noise with unknown variance. We analyze the statistical characteristics of the Discrete Fourier Transform (DFT) of observations and derive the probability distributions of the observations under two hypotheses, which correspond respectively to absence and presence of sinusoidal signals. Considering the leakage effect, we use higher resolution of frequency estimation to estimate the difference between the discrete digital frequency and the real one and compensate the leakage by phase compensation. The detector is further developed based on generalized likelihood ratio test (GLRT) and is a coherent detector that can reduce the noise more rapidly than incoherent detector. The simulation results show that the detector we developed is promising for detecting sinusoidal signals and it outperforms the incoherent detector without using the phase information.